hypre和PETSc中的块局部最优预处理特征值求解器（BLOPEX）
Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc
AI总结：
本文介绍了最近公开发布的软件包BLOPEX，它实现了LOBPCG方法用于对称特征值问题，并集成了hypre和PETSc中的高性能预处理器，通过数值实验展示了其可扩展性。
摘要：
我们描述了我们最近公开发布的软件包Block Locally Optimal Preconditioned Eigenvalue Xolvers（BLOPEX）。BLOPEX可作为独立的串行库使用，也可作为PETSc（“可移植、可扩展的科学计算工具包”，由阿贡国家实验室开发的一套用于可扩展求解偏微分方程及相关问题的通用工具套件）的外部包，并且已内置到{\it hypre}（“高性能预处理器”，由劳伦斯利弗莫尔国家实验室开发的可扩展线性求解器包）中。当前的BLOPEX版本仅包含一个求解器——用于对称特征值问题的局部最优块预处理共轭梯度（LOBPCG）方法。{\it hypre}为用户提供先进的、高质量的线性系统并行预处理器，特别是区域分解和多重网格预处理器。借助BLOPEX，相同的预处理器现在可以高效地用于对称特征值问题。PETSc促进了独立开发的应用程序模块的集成，并严格关注组件互操作性，使得BLOPEX非常容易编译和使用通过PETSc可用的预处理器。我们介绍了用于{\it hypre}和PETSc的BLOPEX中的LOBPCG算法。我们通过在多个分布式和共享内存并行系统（包括Beowulf系统、SUN Fire 880、AMD双核Opteron工作站和IBM BlueGene/L超级计算机）上进行测试，使用PETSc区域分解和{\it hypre}多重网格预处理，数值证明了BLOPEX的可扩展性。我们在一个模型问题——3-D拉普拉斯算子的标准7点有限差分近似上测试BLOPEX，问题规模在$10^5-10^8$范围内。
英文摘要：
We describe our software package Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) publicly released recently. BLOPEX is available as a stand-alone serial library, as an external package to PETSc (``Portable, Extensible Toolkit for Scientific Computation'', a general purpose suite of tools for the scalable solution of partial differential equations and related problems developed by Argonne National Laboratory), and is also built into {\it hypre} (``High Performance Preconditioners'', scalable linear solvers package developed by Lawrence Livermore National Laboratory). The present BLOPEX release includes only one solver--the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for symmetric eigenvalue problems. {\it hypre} provides users with advanced high-quality parallel preconditioners for linear systems, in particular, with domain decomposition and multigrid preconditioners. With BLOPEX, the same preconditioners can now be efficiently used for symmetric eigenvalue problems. PETSc facilitates the integration of independently developed application modules with strict attention to component interoperability, and makes BLOPEX extremely easy to compile and use with preconditioners that are available via PETSc. We present the LOBPCG algorithm in BLOPEX for {\it hypre} and PETSc. We demonstrate numerically the scalability of BLOPEX by testing it on a number of distributed and shared memory parallel systems, including a Beowulf system, SUN Fire 880, an AMD dual-core Opteron workstation, and IBM BlueGene/L supercomputer, using PETSc domain decomposition and {\it hypre} multigrid preconditioning. We test BLOPEX on a model problem, the standard 7-point finite-difference approximation of the 3-D Laplacian, with the problem size in the range $10^5-10^8$.
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